The Iraqi leader spoke after representatives of the Iraqi United Alliance party returned from Iran, where they met with officials in Tehran about Iranian interference in Iraq.

“The Iraqi government thinks the positive relationship with Iran is through the elected government,” Dabbagh said through an interpreter. “There shouldn’t be any financing [or] training for any other side outside the government.”

Coalition and Iraqi officials have accused Iran of training and financing Shiite Iraqi militant elements that coalition military officials call “special groups.” Iran also has smuggled arms -- including explosively formed projectiles designed to pierce armored vehicles -- into Iraq. Extremists are using these weapons against coalition and Iraqi security forces and against innocent Iraqi civilians, officials said.

Illegal militias are a large problem especially in Shiite areas of the country. “It is not possible that there is a parallel force outside the government,” Dabbagh said. “No institute or party can share responsibility with the government. We should be a government of institutions that respect the law and not a government that allows militias and chaos.”

Iraq wants good relations with Iran, and the visit by the Iraqi United Alliance members helped with that dialogue, the spokesman said.

“The mission has been successful, and both sides understand we need security and stability in Iraq,” Dabbagh said. “There can be no stability in Iran unless there is stability in Iraq. That is the message that has been sent and received.”

Iraqi Prime Minister Nouri al-Maliki has ordered a committee to document any Iranian interference in Iraq’s affairs. “The committee will examine all allegations and prove whether this country is trying to interfere or not,” Dabbagh said.

Multinational Force Iraq “is supporting all venues that lead to good dialogue and a peaceful resolution,” Driscoll said.

The admiral also noted a downturn in high-profile al-Qaida attacks in Iraq in April. This reverses the trend since January. “These attacks are used by al-Qaida to try to incite sectarian violence,” Driscoll said. “But by and large, I think the Iraqi people have rejected that failed ideology.”

Al-Qaida is being squeezed out of Iraq, as the terror group neither holds swaths of territory nor controls cities, the admiral said. “But they do remain a very lethal threat and actively pursued out in Anbar, the Diyala River valley and up in Mosul,” he said.

The U.S. drawdown continues on schedule, Driscoll said, with the last of the U.S. surge brigades set to leave Iraq by mid-summer.

“There will be a period of about 45 days where we are going to consolidate and evaluate the situation on the ground and then continue withdrawing troops,” he said.

Any further U.S. withdrawal after the final surge brigades leave will be conditions-based, he noted. “[Commanders will] work closely with Iraqi security forces and with the government of Iraq to make that assessment,” he said.